In the first place, not all brands use these designations in the same way.
Generally, an x
bus mixer has x
busses to sum signal. The simplest is a two bus mixer. Stereo. A left bus and a right bus. You determine what signal goes to which bus with a pan pot.
A 4 bus mixer likely isn't counting the stereo main out, and is referring, instead, to the sub-mix busses. In this case, there would be four separate busses/mixes each with independent gain control. You determine what signal goes to which bus, usually with a switch on each channel, though sometimes it will be a switch and a pan pot, etc.
The x/x
slash designations are still referring to the number of discrete busses, but this time, they're making the distinction between Aux busses and Mix busses (for lack of a better term). Essentially, the number of send
busses that exist. So, a 4/4 console will have 4 aux send busses and also 4 sub-mix busses.
It's an important designation because, although your mixer might have 12 or 18 etc channels, if you only have 4 aux send busses, there will be more sharing between the channels.
In short, those numbers describe the number of discrete, summing, internal pathways that lead to an output.
EDIT
Ok, so after a bit more digging regarding the edit to the original question, I have the answer... at least as it pertains to Behringer, and this particular model (i.e. extrapolate at your own risk)
I asked Behringer. Their response was as follows:
The 2/2 denotes that the mixer is full duplex. What this translates
to is that, via the USB connection, the mixer can transmit and
receive two tracks of audio simultaneously - that would be a stereo
mix both to and from the computer.
So it would seem that throwing a USB interface in there kind of changes the rules of designation.
EDIT
And finally, one last communication from Behringer:
I asked:
Does the 'slash' designation always refer to the USB simultaneous I/O?
Are your analog consoles described with a different nomenclature?
They answered:
The nomenclature of "2/2" is certainly used on Behringer USB mixers,
though it may be different from other manufacturers. The analog
boards have a slightly different designation. The 2442FX, for
instance, is a 4/2 mixer. This means that is has 4 subgroups and 2
main outputs (left and right).
pre
fader. The yellow FX bus ispost
fader only. That is your 2/2. Apparently, Behringer decided that the sub-mix busses and the pre-fader aux busses were the important ones to include in the product name. You are looking for standards where there are none... like I said.